Question 1186092: Mr. and Mrs. Austria love to run around the town. From past experiences, they know that
Mr. Austria can run 6km in the time it takes Mrs. Austria to run 4km. They have decided
that they need to run the same distance, 9km, and finish together. How much of a head
start does Mrs. Austria need for them to finish together
Found 3 solutions by JBnovelwriter, greenestamps, ikleyn:
Answer by JBnovelwriter(34)   (Show Source):
You can put this solution on YOUR website! 4/4=1km
6/4=1.5km per 1km of his (he is .5km faster to go the same 1km as her or basically she goes 2/3's his speed)
9 total km / 1.5 km= 6
9-6=3
so he needs to give her a 3km head start
so for every 2km she runs he is on the 3rd km
so when she is at 4km he's at 6km
so when she is at 6km he's at 9km
that's a 3km gap which is why he needs to give her a 3km head start.
Answer by greenestamps(13214)  (Show Source):
You can put this solution on YOUR website!
New tutor JBnovelwriter has provided a response in which it is not at all clear -- to me, at least -- how he is solving the problem. He apparently likes writing mystery novels, in which the reader has to try to figure out what is going on....
A response on this forum to a reader's question should not read like a mystery novel; it should clearly explain the process for solving the problem.
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Mrs. Austria runs 2/3 as fast as Mr. Austria.
So in the time Mr. Austria runs the full 9km, Mrs. Austria runs only 6km.
Therefore, to finish at the same time, Mrs. Austria must be given a head start of 3km.
Since she runs at 4km/hr, she needs to start the race 3/4 hour (45 minutes) before Mr. Austria to get the required 3km head start.
ANSWER: 45 minutes.
Answer by ikleyn(52898)  (Show Source):
You can put this solution on YOUR website! .
As worded, this problem is self-intersecting,
because one time it says that they decided to run the same distance, but in reality, they run different distances.
It is like self-intersecting street in the city . . .
Had I be a major in such city, I would post a warning signs at such self-intersection points,
for the citizens' safety . . .
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